Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.
Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.
复制标题
DOI：
10.1016/j.cma.2024.116822
复制
发表时间：
2023-08
影响因子：
7.2
通讯作者：
A. Rubaiyat;D. H. Thai;J. Nichols;M. Hutchinson;S. Wallen;Christina J. Naify;Nathan Geib;M. Haberman;G. Rohde
中科院分区：
文献类型：
--
作者：
A. Rubaiyat;D. H. Thai;J. Nichols;M. Hutchinson;S. Wallen;Christina J. Naify;Nathan Geib;M. Haberman;G. Rohde
本文提出了一种新的数据驱动的方法来识别动力系统的偏微分方程（PDE）参数。具体而言，我们采用了一个数学“运输”模型的解决方案的动力系统在特定的空间位置，使我们能够准确地估计模型参数，包括与结构损伤。这是通过一个新开发的数学变换，符号累积分布变换（SCDT），这是一般的非线性参数估计问题转化为一个简单的线性回归。这种方法具有另外的实际优点，即不需要对激励源（或者初始条件）有任何先验知识。通过使用训练数据，我们设计了一个粗略的回归过程，以恢复不同的PDE参数从PDE解决方案在一个单一的位置测量。数值实验表明，所提出的回归过程是能够检测和估计PDE参数的上级精度相比，一些最近开发的机器学习方法。此外，一个公开的数据集上进行的损伤识别实验提供了强有力的证据，所提出的方法的有效性，在结构健康监测（SHM）的应用。所提出的系统识别技术的Python实现被集成为软件包PytransKit（成像和数据科学实验室）的一部分[1]。
This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical “transport” model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring noa prioriknowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method’s effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit (Imaging and data science lab) [1].